Bücher der Reihe Foundations and Trends (R) in Optimization

Reviews the information relaxation approach which works by reducing a complex stochastic Dynamic Programming to a series of scenario-specific deterministic optimization problems solved within a Monte Carlo simulation.

This book is an introduction to Acceleration Methods used in convex optimization that enables the reader to quickly understand the important principles and apply the techniques to their own research.

Explores a class of methods that are capable of formally verifying properties of deep neural networks. The book introduces a unified mathematical framework for verifying neural networks, classify existing methods under this framework, provide pedagogical implementations of existing methods, and compare those methods on a set of benchmark problems.

Presents a comprehensive statistical learning framework that uses Distributionally Robust Optimization (DRO) under the Wasserstein metric to ensure robustness to perturbationsin the data. The authors introduce the reader to the fundamental properties of the Wasserstein metric and the DRO formulation, before explaining the theory in detail.

An atomic decomposition provides a description of the most informative features of a solution or a kind of generalized principal component analysis. In this book, the authors describe the rich convex geometry that underlies atomic decomposition and demonstrate its use in practical examples.

Provides an in-depth overview of the index tracking problem and analyses all the caveats and practical issues an investor might have. Additionally, it provides a unified framework for a large variety of sparse index tracking formulations.

Reviews the theory of low-rank semidefinite programming, presenting theorems that guarantee the existence of a low-rank solution, heuristics for computing low-rank solutions, and algorithms for finding low-rank approximate solutions. The book then presents applications of the theory to trust-region problems and signal processing.

Focuses on optimization as a process. This book is intended to serve as a reference for a self-contained course on online convex optimization and the convex optimization approach to machine learning for the educated graduate student in computer science/electrical engineering/operations research/statistics and related fields.

Covers the theory and applications of chordal graphs, with an emphasis on algorithms developed in the literature on sparse Cholesky factorization. These algorithms are formulated as recursions on elimination trees, supernodal elimination trees, or clique trees associated with the graph.

Discusses different interpretations of proximal operators and algorithms, looks at their connections to many other topics in optimization and applied mathematics, surveys some popular algorithms, and provides a large number of examples of proximal operators that commonly arise in practice.

Presents a fully decentralized method for dynamic network energy management based on messages passing between devices. The book considers a network of devices, such as generators, fixed loads, deferrable loads, and storage devices, each with its own dynamic constraints and objective, connected by AC and DC lines.

Examines dynamic trading of a portfolio of assets in discrete periods over a finite time horizon, with arbitrary time-varying distribution of asset returns. The goal is to maximize the total expected revenue from the portfolio, while respecting constraints on the portfolio like a required terminal portfolio and leverage and risk limits.